Douglas Norman "Doug" Arnold is a mathematician whose research focuses on the numerical analysis of

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s with applications in mechanics and other fields in physics. , he is McKnight Presidential Professor of Mathematics at the University of Minnesota.

Biography

Arnold studied mathematics as an undergraduate at

Brown University Brown University is a private research university in Providence, Rhode Island. Brown is the seventh-oldest institution of higher education in the United States, founded in 1764 as the College in the English Colony of Rhode Island and Providenc ...

, gaining his B.A. in 1975. He continued his studies at the University of Chicago, where he received a Ph.D. in 1979. He then moved to work at the University of Maryland, College Park. In 1989, he moved to

Penn State University The Pennsylvania State University (Penn State or PSU) is a public state-related land-grant research university with campuses and facilities throughout Pennsylvania. Founded in 1855 as the Farmers' High School of Pennsylvania, Penn State became ...

where he occupied a chair until 2002. He became director of the Institute for Mathematics and its Applications (IMA) in Minnesota in 2001. At the end of his term as director of the IMA, he becomes the McKnight Presidential Professor of Mathematics at the University of Minnesota. He served as president of the

Society for Industrial and Applied Mathematics Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific socie ...

in 2009 and 2010. Arnold's research initially focused on the finite element method for the solution of problems in

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

. This expanded to take other applications into account, like the collision of

black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...

s. Especially well known is Arnold's development of the

finite element exterior calculus Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application has been a comprehensive theory for finite element methods in computational electromagnetism, ...

, a discrete version of exterior calculus that can be used to analyze the stability of finite element methods. This was the topic of the plenary lecture Arnold gave at the 2002

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

. Together with a colleague (Jonathan Rogness), Arnold produced a video explaining

Möbius transformation In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form f(z) = \frac of one complex variable ''z''; here the coefficients ''a'', ''b'', ''c'', ''d'' are complex numbers satisfying ''ad'' ...

s which won an honorable mention in a contest sponsored by Science magazine and the National Science Foundation in 2007. The video was watched over a million times at YouTube. Other honors include winning the

International Giovanni Sacchi Landriani Prize The International Giovanni Sacchi Landriani Prize is awarded every two years by the Istituto Lombardo, Accademia di Scienze e Lettere to recognize important original contributions to the field of numerical methods for partial differential equations ...

in 1991, the award of a

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

in 2008 and election as a foreign member of the Norwegian Academy of Science and Letters in 2009. In 2012 he became a fellow of the American Mathematical Society. In 2009, he was named a fellow of the

.SIAM Fellows
/ref> Arnold is married to

Maria-Carme Calderer Maria-Carme T. Calderer (Berga, 1951) is a professor of mathematics at University of Minnesota. Her research concerns applied mathematics. Career Calderer received her Ph.D. from Heriot-Watt University in 1980. She was a postdoctoral researcher ...

, a professor of mathematics at University of Minnesota.

References

External links

Home page at the University of Minnesota
* {{DEFAULTSORT:Arnold, Douglas Norman 20th-century American mathematicians 21st-century American mathematicians Numerical analysts Fellows of the American Mathematical Society Fellows of the Society for Industrial and Applied Mathematics Living people Members of the Norwegian Academy of Science and Letters Presidents of the Society for Industrial and Applied Mathematics Year of birth missing (living people) Brown University alumni University of Chicago alumni